Question

Solve to three significant digits. $$ 13+e^{3 x+5}=23 $$

   Solve to three significant digits.
$$
13+e^{3 x+5}=23
$$

Precalculus

Raymond A. Barnett,… 7th Edition

Chapter 5, Problem 14

Instant Answer

Solved by Expert James Kiss

07/14/2021

Step 1

Step 1: Subtract 13 from both sides of the equation to isolate the exponential term: $$ e^{3x+5} = 23 - 13 $$ which simplifies to: $$ e^{3x+5} = 10 $$ Show more…

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Solve to three significant digits. $$ 13+e^{3 x+5}=23 $$

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Key Concepts

Exponential Equations

Exponential equations are equations in which variables appear in exponents. Solving these equations often requires isolating the exponential part and then applying logarithms to remove the variable from the exponent, enabling further algebraic manipulation.

Natural Logarithms

Natural logarithms are logarithms with base e, and they are particularly useful for solving equations involving the exponential function e^x. The key property ln(e^y) = y allows us to 'undo' the exponential function and isolate the variable in the exponent.

Numerical Approximation and Significant Figures

Numerical approximation involves finding a decimal value for expressions that cannot be simplified exactly. When a problem specifies a certain number of significant digits, the final computed value must be rounded appropriately to reflect the desired precision.

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